Obama aimed to reach out to Putin from Air Force One while on a campaign-style swing to Virginia and Texas, spokesman Josh Earnest told reporters.

"It took a little while to schedule the call," Earnest said. So was the call congratulatory? "I just said he called him."

Putin, a former KGB officer, carried last weekend's elections with more than 63 percent of the votes cast. International election monitors and opponents to the once-and-future president have disputed the fairness of the election. Some world leaders, like British Prime Minister David Cameron, called him early this week but did not congratulate him.

On Wednesday, Putin took a shot at Obama's hometown of Chicago, which will play host in May to the annual NATO summit.

"Yes, they say (Chicago is) good," Putin said. "Al Capone lived there." (This is amusing at least partly because Putin himself once appeared on the cover of the Economist depicted as a 1920s' style gangster, holding a gas pump nozzle instead of a machine gun.)

Despite abundant concerns in Washington that Russia is backsliding from democratic reforms—and that Putin's re-election is a prime example—Obama himself has signaled in recent days that he doesn't want a chill to descend on relations he has worked so hard to "reset" since coming into office three years ago.

On Tuesday, Obama suggested to reporters at his first solo press conference of 2012 that improving ties with Putin had figured into his decision to move a Group of Eight summit from Chicago to the secluded Camp David retreat.

"It will give me a chance to spend time with Mr. Putin," he said.

And later that day, Obama told the Business Roundtable that he would push Congress to repeal a Cold War-era measure, known as the Jackson-Vanik amendment, in order to remove an obstacle to Moscow's entry into the World Trade Organization.

"That's something that we're going to need some help on," he urged the executives in attendance.

That could be something of a struggle in the U.S. Congress, where liberals and conservatives who champion human rights could work to block lifting Jackson-Vanik despite heavy lobbying by U.S. businesses.

"This is not a personality-based policy. It's an approach based on U.S. national interests and the areas where we can reach an agreement," he said. "We obviously look forward to continuing to cooperate and work with Russia where we agree on issues, and that's regardless of who the president is."